Either your stairs are finished in wood or they are constructed of plywood type materials. Homes with carpeted stairs usually have unfinished wood. It is possible to construct a finished looking stairway, but its not a DIY project for most. Pull up a corner of the carpeting carefully and post back with what kind of wood you actually see. If there are exposed nail-heads and rough C or D grade plywood, you would be wasting your time attmptng to refinish the stairs. If the stairs are a solid wood (pine or hardwood) there are ways to dress them up with rounded nosings and other moldings to cover imperfections.